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id="post-meta"><div class="meta-firstline"><span class="post-meta-date"><i class="far fa-calendar-alt fa-fw post-meta-icon"></i><span class="post-meta-label">发表于</span><time class="post-meta-date-created" datetime="2025-05-26T05:13:54.000Z" title="发表于 2025-05-26 13:13:54">2025-05-26</time><span class="post-meta-separator">|</span><i class="fas fa-history fa-fw post-meta-icon"></i><span class="post-meta-label">更新于</span><time class="post-meta-date-updated" datetime="2025-05-26T05:13:54.000Z" title="更新于 2025-05-26 13:13:54">2025-05-26</time></span><span class="post-meta-categories"><span class="post-meta-separator">|</span><i class="fas fa-inbox fa-fw post-meta-icon"></i><a class="post-meta-categories" href="/categories/C-%E8%BF%9B%E9%98%B6/">C++进阶</a></span></div><div class="meta-secondline"><span class="post-meta-separator">|</span><span class="post-meta-wordcount"><i class="far fa-file-word fa-fw post-meta-icon"></i><span class="post-meta-label">总字数:</span><span class="word-count">2687</span><span class="post-meta-separator">|</span><i class="far fa-clock fa-fw post-meta-icon"></i><span class="post-meta-label">阅读时长:</span><span>9分钟</span></span><span class="post-meta-separator">|</span><span class="post-meta-pv-cv" id="" data-flag-title=""><i class="far fa-eye fa-fw post-meta-icon"></i><span class="post-meta-label">浏览量:</span><span id="busuanzi_value_page_pv"><i class="fa-solid fa-spinner fa-spin"></i></span></span></div></div></div></header><main class="layout" id="content-inner"><div id="post"><article class="container post-content" id="article-container"><div id="post-outdate-notice" data="{&quot;limitDay&quot;:365,&quot;messagePrev&quot;:&quot;It has been&quot;,&quot;messageNext&quot;:&quot;days since the last update, the content of the article may be outdated.&quot;,&quot;postUpdate&quot;:&quot;2025-05-26 13:13:54&quot;}" hidden></div><p>位图和布隆过滤器是基于哈希的一种常见应用，通常用来处理大体量数据，提升查找数据的效率</p>
<h1 id="位图"><a href="#位图" class="headerlink" title="位图"></a>位图</h1><p>给40亿个不重复的无符号整数，没排过序。给一个无符号整数，<strong>如何快速判断一个数是否在这40亿个数中?</strong></p>
<p>放在哈希表中去寻找？不，这并不现实，因为哈希表的存储也是需要空间消耗的，况且是 <code>40</code> 亿个数据，如此庞大的数据计算机一般是很难存储</p>
<p>因此就诞生了位图的概念，位图简单来说就是把每个数按照哈希函数的计算，存储到每个比特位上。数据是否在给定的整形数据中，结果是在或者不在，刚好是两种状态，那么可以使用一个二进制比特位来代表数据是否存在的信息，如果二进制比特位为 <code>1</code>，代表存在，为 <code>0</code> 代表不存在</p>
<p><img src= "" data-lazy-src="https://picture-bed000.oss-cn-shenzhen.aliyuncs.com/395fec634dcb4edbacaec25f189589ad.png" alt="在这里插入图片描述"></p>
<h2 id="位图的结构"><a href="#位图的结构" class="headerlink" title="位图的结构"></a>位图的结构</h2><figure class="highlight cpp"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">template</span>&lt;<span class="type">size_t</span> N&gt;</span><br><span class="line"><span class="keyword">class</span> <span class="title class_">bitset</span></span><br><span class="line">&#123;</span><br><span class="line"><span class="keyword">public</span>:</span><br><span class="line">	<span class="built_in">bitset</span>()</span><br><span class="line">	&#123;</span><br><span class="line">		_a.<span class="built_in">resize</span>(N / <span class="number">32</span> + <span class="number">1</span>);</span><br><span class="line">	&#125;</span><br><span class="line"><span class="keyword">private</span>:</span><br><span class="line">	vector&lt;<span class="type">int</span>&gt; _a;</span><br><span class="line">&#125;;</span><br></pre></td></tr></table></figure>

<p>开辟一个 <code>vector</code> 数组 <code>_a</code>，这里我们以 <code>int</code> 作为位图的基本单位，那么就是把每个数据存储到 <code>int</code> 的比特位上</p>
<p>🔥<strong>值得注意的是：</strong> <code>resize</code> 的时候无论如何都要加 <code>1</code>，比如 <code>100</code> 个数据，除以 <code>32</code>，等于 <code>3</code>，余 <code>4</code>，那么就需要多一个 <code>int</code> 空间来存储，不能说每次都卡好刚好 <code>32</code> 整除</p>
<h2 id="位图映射的比特位标记成1"><a href="#位图映射的比特位标记成1" class="headerlink" title="位图映射的比特位标记成1"></a>位图映射的比特位标记成1</h2><figure class="highlight cpp"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br></pre></td><td class="code"><pre><span class="line"><span class="comment">// x映射的那个标记成1</span></span><br><span class="line"><span class="function"><span class="type">void</span> <span class="title">set</span><span class="params">(<span class="type">size_t</span> x)</span></span></span><br><span class="line"><span class="function"></span>&#123;</span><br><span class="line">	<span class="type">size_t</span> i = x / <span class="number">32</span>;</span><br><span class="line">	<span class="type">size_t</span> j = x % <span class="number">32</span>;</span><br><span class="line"></span><br><span class="line">	_a[i] |= (<span class="number">1</span> &lt;&lt; j);</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>

<p><code>i</code> 用于确定在第几个 <code>int</code> 里，<code>j</code> 用于确定在第几个 <code>int</code> 的第几位上</p>
<p><img src= "" data-lazy-src="https://picture-bed000.oss-cn-shenzhen.aliyuncs.com/a7f777c3c85746219bae89507ed646a1.png" alt="在这里插入图片描述"></p>
<p>二进制位从右到左是最低位到最高位，所以左移即可</p>
<h2 id="位图映射的比特位标记成0"><a href="#位图映射的比特位标记成0" class="headerlink" title="位图映射的比特位标记成0"></a>位图映射的比特位标记成0</h2><figure class="highlight cpp"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br></pre></td><td class="code"><pre><span class="line"><span class="comment">// x映射的那个标记成0</span></span><br><span class="line"><span class="function"><span class="type">void</span> <span class="title">reset</span><span class="params">(<span class="type">size_t</span> x)</span></span></span><br><span class="line"><span class="function"></span>&#123;</span><br><span class="line">	<span class="type">size_t</span> i = x / <span class="number">32</span>;</span><br><span class="line">	<span class="type">size_t</span> j = x % <span class="number">32</span>;</span><br><span class="line"></span><br><span class="line">	_a[i] &amp;= (~(<span class="number">1</span> &lt;&lt; j));</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>

<p>同理，因为按位与是有 <code>0</code> 就是 <code>0</code>，直接计算即可</p>
<p><img src= "" data-lazy-src="https://picture-bed000.oss-cn-shenzhen.aliyuncs.com/bb33ae75e3c947bfa16f553f61744dab.png" alt="在这里插入图片描述"></p>
<h2 id="位图映射判断为1-or-0"><a href="#位图映射判断为1-or-0" class="headerlink" title="位图映射判断为1 or 0"></a>位图映射判断为1 or 0</h2><figure class="highlight cpp"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br></pre></td><td class="code"><pre><span class="line"><span class="function"><span class="type">bool</span> <span class="title">test</span><span class="params">(<span class="type">size_t</span> x)</span></span></span><br><span class="line"><span class="function"></span>&#123;</span><br><span class="line">	<span class="type">size_t</span> i = x / <span class="number">32</span>;</span><br><span class="line">	<span class="type">size_t</span> j = x % <span class="number">32</span>;</span><br><span class="line"></span><br><span class="line">	<span class="keyword">return</span> _a[i] &amp; (<span class="number">1</span> &lt;&lt; j);</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>

<p>注意这里是 <code>&amp;</code>，而不是 <code>&amp;=</code>，因为只需要判断，而不是修改</p>
<p>位图通常不支持删除功能，因为没有必要删除</p>
<h1 id="布隆过滤器"><a href="#布隆过滤器" class="headerlink" title="布隆过滤器"></a>布隆过滤器</h1><p><img src= "" data-lazy-src="https://picture-bed000.oss-cn-shenzhen.aliyuncs.com/557968fe3960420491df57c4898dc315.png" alt="在这里插入图片描述"></p>
<p>我们在存储字符串数据时，是通过计算这个字符串的ASC||码值之和，然后通过哈希函数计算存入的，但是这可能会产生哈希冲突，但是数据量太大了，无法通过常规的方法解决</p>
<p>那么最简单的方法就是降低误判率，通过多个不同哈希函数计算，将一个值映射多个位置，这样不至于每次查找都会产生冲突</p>
<ol>
<li>用哈希表存储用户记录，缺点：浪费空间</li>
<li>用位图存储用户记录，缺点：位图一般只能处理整形，如果内容编号是字符串，就无法处理了</li>
<li>将哈希与位图结合，即布隆过滤器</li>
</ol>
<p><img src= "" data-lazy-src="https://picture-bed000.oss-cn-shenzhen.aliyuncs.com/2560b1740d674aed8fa1155e8190641d.png" alt="在这里插入图片描述"></p>
<p><strong>再举个现实点的例子，就能理解布隆过滤器存在的必要：</strong></p>
<p><img src= "" data-lazy-src="https://picture-bed000.oss-cn-shenzhen.aliyuncs.com/83296ed5021e460ea6cd375b49354de8.png" alt="在这里插入图片描述"></p>
<p>比如我们在注册账号昵称时，会显示是否已经被取过，先在布隆过滤器中进行查找，<code>若不在</code>，那么成功注册；<code>如果在</code>，那么就到数据库中查询，这样能减少数据库查询次数，降低负载压力，提升整体查询效率</p>
<h2 id="布隆过滤器的结构"><a href="#布隆过滤器的结构" class="headerlink" title="布隆过滤器的结构"></a>布隆过滤器的结构</h2><figure class="highlight cpp"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">template</span>&lt;<span class="type">size_t</span> N,</span><br><span class="line">    <span class="keyword">class</span> <span class="title class_">K</span> = string,</span><br><span class="line">    <span class="keyword">class</span> Hash1 = BKDRHash,</span><br><span class="line">    <span class="keyword">class</span> Hash2 = APHash,</span><br><span class="line">    <span class="keyword">class</span> Hash3 = DJBHash&gt;</span><br><span class="line"><span class="keyword">class</span> BloomFilter</span><br><span class="line">&#123;</span><br><span class="line"><span class="keyword">private</span>:</span><br><span class="line">    bitset&lt;N&gt; _bs;</span><br><span class="line">&#125;;</span><br></pre></td></tr></table></figure>

<p><code>Hash1</code>、<code>Hash2</code>、<code>Hash3</code> 是用于计算 <code>string</code> 存储的哈希函数，<code>stl</code> 库里是有 <code>bitset</code> 使用的，直接开辟位图空间即可</p>
<blockquote>
<p>传送门：<a target="_blank" rel="noopener" href="https://www.cnblogs.com/-clq/archive/2012/05/31/2528153.html">字符串Hash函数对比</a></p>
</blockquote>
<h2 id="布隆过滤器的哈希函数"><a href="#布隆过滤器的哈希函数" class="headerlink" title="布隆过滤器的哈希函数"></a>布隆过滤器的哈希函数</h2><figure class="highlight cpp"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br><span class="line">41</span><br><span class="line">42</span><br><span class="line">43</span><br><span class="line">44</span><br><span class="line">45</span><br><span class="line">46</span><br><span class="line">47</span><br><span class="line">48</span><br><span class="line">49</span><br><span class="line">50</span><br><span class="line">51</span><br><span class="line">52</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">struct</span> <span class="title class_">BKDRHash</span></span><br><span class="line">&#123;</span><br><span class="line">    <span class="function"><span class="type">size_t</span> <span class="title">operator</span><span class="params">()</span><span class="params">(<span class="type">const</span> string&amp; str)</span></span></span><br><span class="line"><span class="function">    </span>&#123;</span><br><span class="line">        <span class="type">size_t</span> hash = <span class="number">0</span>;</span><br><span class="line">        <span class="keyword">for</span> (<span class="keyword">auto</span> ch : str)</span><br><span class="line">        &#123;</span><br><span class="line">            hash = hash * <span class="number">131</span> + ch;</span><br><span class="line">        &#125;</span><br><span class="line"></span><br><span class="line">        <span class="comment">//cout &lt;&lt;&quot;BKDRHash:&quot; &lt;&lt; hash &lt;&lt; endl;</span></span><br><span class="line">        <span class="keyword">return</span> hash;</span><br><span class="line">    &#125;</span><br><span class="line">&#125;;</span><br><span class="line"></span><br><span class="line"><span class="keyword">struct</span> <span class="title class_">APHash</span></span><br><span class="line">&#123;</span><br><span class="line">    <span class="function"><span class="type">size_t</span> <span class="title">operator</span><span class="params">()</span><span class="params">(<span class="type">const</span> string&amp; str)</span></span></span><br><span class="line"><span class="function">    </span>&#123;</span><br><span class="line">        <span class="type">size_t</span> hash = <span class="number">0</span>;</span><br><span class="line">        <span class="keyword">for</span> (<span class="type">size_t</span> i = <span class="number">0</span>; i &lt; str.<span class="built_in">size</span>(); i++)</span><br><span class="line">        &#123;</span><br><span class="line">            <span class="type">size_t</span> ch = str[i];</span><br><span class="line">            <span class="keyword">if</span> ((i &amp; <span class="number">1</span>) == <span class="number">0</span>)</span><br><span class="line">            &#123;</span><br><span class="line">                hash ^= ((hash &lt;&lt; <span class="number">7</span>) ^ ch ^ (hash &gt;&gt; <span class="number">3</span>));</span><br><span class="line">            &#125;</span><br><span class="line">            <span class="keyword">else</span></span><br><span class="line">            &#123;</span><br><span class="line">                hash ^= (~((hash &lt;&lt; <span class="number">11</span>) ^ ch ^ (hash &gt;&gt; <span class="number">5</span>)));</span><br><span class="line">            &#125;</span><br><span class="line">        &#125;</span><br><span class="line"></span><br><span class="line">        <span class="comment">//cout &lt;&lt; &quot;APHash:&quot; &lt;&lt; hash &lt;&lt; endl;</span></span><br><span class="line">        <span class="keyword">return</span> hash;</span><br><span class="line">    &#125;</span><br><span class="line">&#125;;</span><br><span class="line"></span><br><span class="line"><span class="keyword">struct</span> <span class="title class_">DJBHash</span></span><br><span class="line">&#123;</span><br><span class="line">    <span class="function"><span class="type">size_t</span> <span class="title">operator</span><span class="params">()</span><span class="params">(<span class="type">const</span> string&amp; str)</span></span></span><br><span class="line"><span class="function">    </span>&#123;</span><br><span class="line">        <span class="type">size_t</span> hash = <span class="number">5381</span>;</span><br><span class="line">        <span class="keyword">for</span> (<span class="keyword">auto</span> ch : str)</span><br><span class="line">        &#123;</span><br><span class="line">            hash += (hash &lt;&lt; <span class="number">5</span>) + ch;</span><br><span class="line">        &#125;</span><br><span class="line"></span><br><span class="line">        <span class="comment">//cout &lt;&lt; &quot;DJBHash:&quot; &lt;&lt; hash &lt;&lt; endl;</span></span><br><span class="line">        <span class="keyword">return</span> hash;</span><br><span class="line">    &#125;</span><br><span class="line">&#125;;</span><br></pre></td></tr></table></figure>

<p>选取了三种计算冲突较小的哈希函数算法进行计算，因为需要多处使用，以仿函数的形式更加方便快捷</p>
<h2 id="布隆过滤器的插入"><a href="#布隆过滤器的插入" class="headerlink" title="布隆过滤器的插入"></a>布隆过滤器的插入</h2><figure class="highlight cpp"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br></pre></td><td class="code"><pre><span class="line"><span class="function"><span class="type">void</span> <span class="title">Set</span><span class="params">(<span class="type">const</span> K&amp; key)</span></span></span><br><span class="line"><span class="function"></span>&#123;</span><br><span class="line">    <span class="type">size_t</span> hash1 = <span class="built_in">Hash1</span>()(key) % N;</span><br><span class="line">    _bs.<span class="built_in">set</span>(hash1);</span><br><span class="line"></span><br><span class="line">    <span class="type">size_t</span> hash2 = <span class="built_in">Hash2</span>()(key) % N;</span><br><span class="line">    _bs.<span class="built_in">set</span>(hash2);</span><br><span class="line"></span><br><span class="line">    <span class="type">size_t</span> hash3 = <span class="built_in">Hash3</span>()(key) % N;</span><br><span class="line">    _bs.<span class="built_in">set</span>(hash3);</span><br><span class="line"></span><br><span class="line">    <span class="comment">/* cout &lt;&lt; hash1 &lt;&lt; endl;</span></span><br><span class="line"><span class="comment">     cout &lt;&lt; hash2 &lt;&lt; endl;</span></span><br><span class="line"><span class="comment">     cout &lt;&lt; hash3 &lt;&lt; endl &lt;&lt; endl;*/</span></span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>

<p>由于是以仿函数的方式进行，<code>Hash1()</code> 是匿名对象，有了对象才能以函数的形式调用参数</p>
<h2 id="布隆过滤器映射判断为true-or-false"><a href="#布隆过滤器映射判断为true-or-false" class="headerlink" title="布隆过滤器映射判断为true or false"></a>布隆过滤器映射判断为true or false</h2><figure class="highlight cpp"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br></pre></td><td class="code"><pre><span class="line"><span class="function"><span class="type">bool</span> <span class="title">Test</span><span class="params">(<span class="type">const</span> K&amp; key)</span></span></span><br><span class="line"><span class="function"></span>&#123;</span><br><span class="line">    <span class="type">size_t</span> hash1 = <span class="built_in">Hash1</span>()(key) % N;</span><br><span class="line">    <span class="keyword">if</span> (_bs.<span class="built_in">test</span>(hash1) == <span class="literal">false</span>)</span><br><span class="line">        <span class="keyword">return</span> <span class="literal">false</span>;</span><br><span class="line"></span><br><span class="line">    <span class="type">size_t</span> hash2 = <span class="built_in">Hash2</span>()(key) % N;</span><br><span class="line">    <span class="keyword">if</span> (_bs.<span class="built_in">test</span>(hash2) == <span class="literal">false</span>)</span><br><span class="line">        <span class="keyword">return</span> <span class="literal">false</span>;</span><br><span class="line"></span><br><span class="line">    <span class="type">size_t</span> hash3 = <span class="built_in">Hash3</span>()(key) % N;</span><br><span class="line">    <span class="keyword">if</span> (_bs.<span class="built_in">test</span>(hash3) == <span class="literal">false</span>)</span><br><span class="line">        <span class="keyword">return</span> <span class="literal">false</span>;</span><br><span class="line"></span><br><span class="line">    <span class="keyword">return</span> <span class="literal">true</span>;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>

<h2 id="布隆过滤器的优缺点"><a href="#布隆过滤器的优缺点" class="headerlink" title="布隆过滤器的优缺点"></a>布隆过滤器的优缺点</h2><p>🚩<strong>优点：</strong></p>
<ol>
<li>增加和查询元素的时间复杂度为: <code>O(K)</code>, ( <code>K</code> 为哈希函数的个数，一般比较小)，与数据量大小无关</li>
<li>哈希函数相互之间没有关系，方便硬件并行运算</li>
<li>布隆过滤器不需要存储元素本身，在某些对保密要求比较严格的场合有很大优势</li>
<li>在能够承受一定的误判时，布隆过滤器比其他数据结构有这很大的空间优势</li>
<li>数据量很大时，布隆过滤器可以表示全集，其他数据结构不能</li>
<li>使用同一组散列函数的布隆过滤器可以进行交、并、差运算</li>
</ol>
<p>🚩<strong>缺点：</strong></p>
<ol>
<li>有误判率，即存在假阳性(<code>False Position</code>)，即不能准确判断元素是否在集合中(补救方法：再建立一个白名单，存储可能会误判的数据)</li>
<li>不能获取元素本身</li>
<li>一般情况下不能从布隆过滤器中删除元素</li>
<li>如果采用计数方式删除，可能会存在计数回绕问题</li>
</ol>
<h1 id="常见面试题"><a href="#常见面试题" class="headerlink" title="常见面试题"></a>常见面试题</h1><h2 id="哈希切割"><a href="#哈希切割" class="headerlink" title="哈希切割"></a>哈希切割</h2><h3 id="问题一"><a href="#问题一" class="headerlink" title="问题一"></a>问题一</h3><p>给一个超过 <code>100G</code> 大小的 <code>log file</code>，<code>log</code> 中存着 <code>IP</code> 地址, 设计算法找到出现次数最多的 <code>IP</code> 地址？</p>
<p>🛜<strong>解决方法：</strong></p>
<p>对于超过 <code>100G</code> 的日志文件，直接加载到内存是不可行的，既然大的不行，就把文件分割为小文件一个个进行</p>
<p>使用哈希函数计算将 <code>IP</code> 映射到不同的小文件中，确保相同 <code>IP</code> 进入同一个文件，对每个小文件，使用哈希表统计 <code>IP</code> 频率，合并所有小文件的统计结果，就能找出出现次数最多的 <code>IP</code></p>
<h3 id="问题二"><a href="#问题二" class="headerlink" title="问题二"></a>问题二</h3><p>与上题条件相同，如何找到 <code>top K</code> 的 <code>IP</code> ？</p>
<p>🛜<strong>解决方法：</strong></p>
<p>既然相同 <code>IP</code> 一定进入同一个小文件，用 <code>map</code> 去统计每个文件中 <code>IP</code> 出现的次数即可</p>
<h2 id="位图应用"><a href="#位图应用" class="headerlink" title="位图应用"></a>位图应用</h2><h3 id="问题一-1"><a href="#问题一-1" class="headerlink" title="问题一"></a>问题一</h3><p>给定 <code>100</code> 亿个整数，设计算法找到只出现一次的整数？</p>
<p>🛜<strong>解决方法：</strong></p>
<p>对于 <code>100</code> 亿个整数（约 <code>40GB</code> 数据），直接加载到内存显然不可行。我们可以使用 <code>位图</code> 和 <code>哈希分治</code> 相结合的方法高效解决这个问题——<code>双位图法</code></p>
<p><img src= "" data-lazy-src="https://i-blog.csdnimg.cn/direct/46b9ccde77224e5e959fffd73ef7bb16.png" alt="在这里插入图片描述"><br>使用两个位图，每个整数对应两位：</p>
<ul>
<li><code>00</code>：整数未出现</li>
<li><code>01</code>：整数出现 <code>1</code> 次</li>
<li><code>10</code>：整数出现 <code>2</code> 次及以上</li>
</ul>
<p>假设计算出第一个数据映射第一个位置，且第一次出现，则上面的位图第一位设置为 <code>0</code>，下面位图的第一位设置为 <code>1</code>。其他情况依次类推</p>
<figure class="highlight cpp"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">template</span>&lt;<span class="type">size_t</span> N&gt;</span><br><span class="line"><span class="keyword">class</span> <span class="title class_">twobitset</span></span><br><span class="line">&#123;</span><br><span class="line"><span class="keyword">public</span>:</span><br><span class="line">	<span class="function"><span class="type">void</span> <span class="title">set</span><span class="params">(<span class="type">size_t</span> x)</span></span></span><br><span class="line"><span class="function">	</span>&#123;</span><br><span class="line">		<span class="comment">// 00 -&gt; 01</span></span><br><span class="line">		<span class="keyword">if</span> (!_bs<span class="number">1.</span><span class="built_in">test</span>(x) &amp;&amp; !_bs<span class="number">2.</span><span class="built_in">test</span>(x))</span><br><span class="line">		&#123;</span><br><span class="line">			_bs<span class="number">2.</span><span class="built_in">set</span>(x);</span><br><span class="line">		&#125; <span class="comment">// 01 -&gt; 10</span></span><br><span class="line">		<span class="keyword">else</span> <span class="keyword">if</span> (!_bs<span class="number">1.</span><span class="built_in">test</span>(x) &amp;&amp; _bs<span class="number">2.</span><span class="built_in">test</span>(x))</span><br><span class="line">		&#123;</span><br><span class="line">			_bs<span class="number">1.</span><span class="built_in">set</span>(x);</span><br><span class="line">			_bs<span class="number">2.</span><span class="built_in">reset</span>(x);</span><br><span class="line">		&#125;</span><br><span class="line">		<span class="comment">// 本身10代表出现2次及以上，就不变了</span></span><br><span class="line">	&#125;</span><br><span class="line"></span><br><span class="line">	<span class="function"><span class="type">bool</span> <span class="title">is_once</span><span class="params">(<span class="type">size_t</span> x)</span></span></span><br><span class="line"><span class="function">	</span>&#123;</span><br><span class="line">		<span class="keyword">return</span> !_bs<span class="number">1.</span><span class="built_in">test</span>(x) &amp;&amp; _bs<span class="number">2.</span><span class="built_in">test</span>(x);</span><br><span class="line">	&#125;</span><br><span class="line"><span class="keyword">private</span>:</span><br><span class="line">	bitset&lt;N&gt; _bs1;</span><br><span class="line">	bitset&lt;N&gt; _bs2;</span><br><span class="line">&#125;;</span><br></pre></td></tr></table></figure>

<p>最后遍历位图对每一位进行 <code>is_once</code> 函数的判断，符合一次的存入哈希表即可</p>
<h3 id="问题二-1"><a href="#问题二-1" class="headerlink" title="问题二"></a>问题二</h3><p>给两个文件，分别有 <code>100</code> 亿个整数，我们只有 <code>1G</code> 内存，如何找到两个文件交集？</p>
<p>🛜<strong>解决方法：</strong> </p>
<p>还是利用两个位图的方式解决，一个文件映射一个位图，对应的位置 <code>&amp;</code> 按位与一下，两个位置都为 <code>1</code>，则这个位置是交集，注意存储的值应该放在 <code>set</code> 里去重</p>
<h3 id="问题三"><a href="#问题三" class="headerlink" title="问题三"></a>问题三</h3><p><code>1</code> 个文件有 <code>100</code> 亿个 <code>int</code>，<code>1G</code> 内存，设计算法找到出现次数不超过 <code>2</code> 次的所有整数</p>
<p>🛜<strong>解决方法：</strong> </p>
<p>和问题一的方法是一样的，只不过改一下表示方法而已</p>
<ul>
<li><code>00</code>：整数未出现</li>
<li><code>01</code>：整数出现 <code>1</code> 次</li>
<li><code>10</code>：整数出现 <code>2</code> 次</li>
<li><code>11</code>：整数出现 <code>3</code> 次及以上</li>
</ul>
<h2 id="布隆过滤器应用"><a href="#布隆过滤器应用" class="headerlink" title="布隆过滤器应用"></a>布隆过滤器应用</h2><h3 id="问题一-2"><a href="#问题一-2" class="headerlink" title="问题一"></a>问题一</h3><p>给两个文件，分别有 <code>100</code>亿个 <code>query</code>，我们只有 <code>1G</code> 内存，如何找到两个文件交集？分别给出精确算法和近似算法</p>
<p>🛜<strong>解决方法：</strong> </p>
<p><strong>近似算法：</strong></p>
<p>用文件 <code>A</code> 的所有 <code>query</code> 构建布隆过滤器，遍历文件 <code>B</code> 的每个 <code>query</code>，判断是否可能在 <code>A</code> 中，对布隆过滤器返回 “可能存在” 的 <code>query</code>，再在文件 <code>A</code> 中精确验证，但是这种方法并不百分百准确，可能存在误判</p>
<p><strong>精确算法：</strong></p>
<p><img src= "" data-lazy-src="https://i-blog.csdnimg.cn/direct/2eac9dea54dd4a7a8e29a375bebf6e2b.png" alt="在这里插入图片描述"></p>
<p>将 <code>A</code>、<code>B</code> 文件都分割为同样数量的小文件，都上好编号，因为经过相同哈希函数计算，所以 <code>A</code> 和 <code>B</code> 中相同的 <code>query</code> 必定分别进入 <code>Ai</code> 和 <code>Bi</code> 文件中，因此 <code>A0</code> 和 <code>B0</code> 比较，<code>A1</code> 和 <code>B1</code> 进行比较，以此类推即可</p>
<p><img src= "" data-lazy-src="https://i-blog.csdnimg.cn/direct/e658858eb2924a15a9cc47c65eaf490b.png" alt="在这里插入图片描述"></p>
<h3 id="问题二-2"><a href="#问题二-2" class="headerlink" title="问题二"></a>问题二</h3><p>如何扩展 <code>BloomFilter</code> 使得它支持删除元素的操作?</p>
<p>🛜<strong>解决方法：</strong> </p>
<p>将标准布隆过滤器的每个二进制位扩展为一个小计数器（通常 <code>4-8</code> 位），当插入元素时增加计数器，删除时减少计数器。只有当计数器为 <code>0</code> 时，才表示该位置未被占用</p>
<hr>
<h1 id="希望读者们多多三连支持"><a href="#希望读者们多多三连支持" class="headerlink" title="希望读者们多多三连支持"></a>希望读者们多多三连支持</h1><h1 id="小编会继续更新"><a href="#小编会继续更新" class="headerlink" title="小编会继续更新"></a>小编会继续更新</h1><h1 id="你们的鼓励就是我前进的动力！"><a href="#你们的鼓励就是我前进的动力！" class="headerlink" title="你们的鼓励就是我前进的动力！"></a>你们的鼓励就是我前进的动力！</h1><p><img src= "" data-lazy-src="https://picture-bed000.oss-cn-shenzhen.aliyuncs.com/8c697c8f7d52431b93f6f738ac7850f1.png" alt="请添加图片描述"></p>
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right;&#125;double Add(double left, double right)&#123;	 cout &lt;&lt; &quot;double Add(double left, double right)&quot; &lt;&lt; endl;	 return left + right;&#125; 一个函数类型为 int ，一个函数类型为 double...</div></div></div></a><a class="pagination-related" href="/2024/11/29/CPP%E5%88%9D%E9%98%B6/C++%E5%85%A5%E9%97%A8%EF%BC%88%E4%B8%8B%EF%BC%89/" title="C++命运石之门代码抉择：C++入门（下）"><img class="cover" src= "" data-lazy-src="https://picture-bed000.oss-cn-shenzhen.aliyuncs.com/%E5%BE%AE%E4%BF%A1%E5%9B%BE%E7%89%87_20241129124329.jpg" alt="cover"><div class="info text-center"><div class="info-1"><div class="info-item-1"><i class="far fa-calendar-alt fa-fw"></i> 2024-11-29</div><div class="info-item-2">C++命运石之门代码抉择：C++入门（下）</div></div><div class="info-2"><div class="info-item-1">C语言过渡到C++(下)auto 关键字(C++11)为什么要用 auto？随着后续 C++ 语法的越来越深入，类型的长度可能会越来越长，因为在一些情境下是不允许把全部命名空间全部打开，所以在写类型时可能会遇到以下问题： • 类型难于拼写• 含义不明确导致容易出错 ⌨️比如后续学到迭代器有这么个类型 1std::map&lt;std::string, std::string&gt;::iterator 或许有聪明的人会想到直接用 typedef 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class="toc-text">位图</span></a><ol class="toc-child"><li class="toc-item toc-level-2"><a class="toc-link" href="#%E4%BD%8D%E5%9B%BE%E7%9A%84%E7%BB%93%E6%9E%84"><span class="toc-number">1.1.</span> <span class="toc-text">位图的结构</span></a></li><li class="toc-item toc-level-2"><a class="toc-link" href="#%E4%BD%8D%E5%9B%BE%E6%98%A0%E5%B0%84%E7%9A%84%E6%AF%94%E7%89%B9%E4%BD%8D%E6%A0%87%E8%AE%B0%E6%88%901"><span class="toc-number">1.2.</span> <span class="toc-text">位图映射的比特位标记成1</span></a></li><li class="toc-item toc-level-2"><a class="toc-link" href="#%E4%BD%8D%E5%9B%BE%E6%98%A0%E5%B0%84%E7%9A%84%E6%AF%94%E7%89%B9%E4%BD%8D%E6%A0%87%E8%AE%B0%E6%88%900"><span class="toc-number">1.3.</span> <span class="toc-text">位图映射的比特位标记成0</span></a></li><li class="toc-item toc-level-2"><a class="toc-link" href="#%E4%BD%8D%E5%9B%BE%E6%98%A0%E5%B0%84%E5%88%A4%E6%96%AD%E4%B8%BA1-or-0"><span class="toc-number">1.4.</span> <span class="toc-text">位图映射判断为1 or 0</span></a></li></ol></li><li class="toc-item toc-level-1"><a class="toc-link" href="#%E5%B8%83%E9%9A%86%E8%BF%87%E6%BB%A4%E5%99%A8"><span class="toc-number">2.</span> <span class="toc-text">布隆过滤器</span></a><ol class="toc-child"><li class="toc-item toc-level-2"><a class="toc-link" href="#%E5%B8%83%E9%9A%86%E8%BF%87%E6%BB%A4%E5%99%A8%E7%9A%84%E7%BB%93%E6%9E%84"><span class="toc-number">2.1.</span> <span class="toc-text">布隆过滤器的结构</span></a></li><li class="toc-item toc-level-2"><a class="toc-link" href="#%E5%B8%83%E9%9A%86%E8%BF%87%E6%BB%A4%E5%99%A8%E7%9A%84%E5%93%88%E5%B8%8C%E5%87%BD%E6%95%B0"><span class="toc-number">2.2.</span> <span class="toc-text">布隆过滤器的哈希函数</span></a></li><li class="toc-item toc-level-2"><a class="toc-link" href="#%E5%B8%83%E9%9A%86%E8%BF%87%E6%BB%A4%E5%99%A8%E7%9A%84%E6%8F%92%E5%85%A5"><span class="toc-number">2.3.</span> <span class="toc-text">布隆过滤器的插入</span></a></li><li class="toc-item toc-level-2"><a class="toc-link" href="#%E5%B8%83%E9%9A%86%E8%BF%87%E6%BB%A4%E5%99%A8%E6%98%A0%E5%B0%84%E5%88%A4%E6%96%AD%E4%B8%BAtrue-or-false"><span class="toc-number">2.4.</span> <span class="toc-text">布隆过滤器映射判断为true or false</span></a></li><li class="toc-item toc-level-2"><a class="toc-link" href="#%E5%B8%83%E9%9A%86%E8%BF%87%E6%BB%A4%E5%99%A8%E7%9A%84%E4%BC%98%E7%BC%BA%E7%82%B9"><span class="toc-number">2.5.</span> <span class="toc-text">布隆过滤器的优缺点</span></a></li></ol></li><li class="toc-item toc-level-1"><a class="toc-link" href="#%E5%B8%B8%E8%A7%81%E9%9D%A2%E8%AF%95%E9%A2%98"><span class="toc-number">3.</span> <span class="toc-text">常见面试题</span></a><ol class="toc-child"><li class="toc-item toc-level-2"><a class="toc-link" href="#%E5%93%88%E5%B8%8C%E5%88%87%E5%89%B2"><span class="toc-number">3.1.</span> <span class="toc-text">哈希切割</span></a><ol class="toc-child"><li class="toc-item toc-level-3"><a class="toc-link" href="#%E9%97%AE%E9%A2%98%E4%B8%80"><span class="toc-number">3.1.1.</span> <span class="toc-text">问题一</span></a></li><li class="toc-item toc-level-3"><a class="toc-link" href="#%E9%97%AE%E9%A2%98%E4%BA%8C"><span class="toc-number">3.1.2.</span> <span class="toc-text">问题二</span></a></li></ol></li><li class="toc-item toc-level-2"><a class="toc-link" href="#%E4%BD%8D%E5%9B%BE%E5%BA%94%E7%94%A8"><span class="toc-number">3.2.</span> <span class="toc-text">位图应用</span></a><ol class="toc-child"><li class="toc-item toc-level-3"><a class="toc-link" href="#%E9%97%AE%E9%A2%98%E4%B8%80-1"><span class="toc-number">3.2.1.</span> <span class="toc-text">问题一</span></a></li><li class="toc-item toc-level-3"><a class="toc-link" href="#%E9%97%AE%E9%A2%98%E4%BA%8C-1"><span class="toc-number">3.2.2.</span> <span class="toc-text">问题二</span></a></li><li class="toc-item toc-level-3"><a class="toc-link" href="#%E9%97%AE%E9%A2%98%E4%B8%89"><span class="toc-number">3.2.3.</span> <span class="toc-text">问题三</span></a></li></ol></li><li class="toc-item toc-level-2"><a class="toc-link" href="#%E5%B8%83%E9%9A%86%E8%BF%87%E6%BB%A4%E5%99%A8%E5%BA%94%E7%94%A8"><span class="toc-number">3.3.</span> <span class="toc-text">布隆过滤器应用</span></a><ol class="toc-child"><li class="toc-item toc-level-3"><a class="toc-link" href="#%E9%97%AE%E9%A2%98%E4%B8%80-2"><span class="toc-number">3.3.1.</span> <span class="toc-text">问题一</span></a></li><li class="toc-item toc-level-3"><a class="toc-link" href="#%E9%97%AE%E9%A2%98%E4%BA%8C-2"><span class="toc-number">3.3.2.</span> <span class="toc-text">问题二</span></a></li></ol></li></ol></li><li class="toc-item toc-level-1"><a class="toc-link" href="#%E5%B8%8C%E6%9C%9B%E8%AF%BB%E8%80%85%E4%BB%AC%E5%A4%9A%E5%A4%9A%E4%B8%89%E8%BF%9E%E6%94%AF%E6%8C%81"><span class="toc-number">4.</span> <span class="toc-text">希望读者们多多三连支持</span></a></li><li class="toc-item toc-level-1"><a class="toc-link" href="#%E5%B0%8F%E7%BC%96%E4%BC%9A%E7%BB%A7%E7%BB%AD%E6%9B%B4%E6%96%B0"><span class="toc-number">5.</span> <span class="toc-text">小编会继续更新</span></a></li><li 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